Boundary unique continuation for the Laplace equation and the biharmonic operator

Abstract

. We establish results on unique continuation at the boundary for the solutions of ∆ u = f, f harmonic, and the biharmonic equation ∆ 2 u = 0. The work is motivated by analogous results proved for harmonic functions by X. Huang et al in [HK1], [HK2], and [HKMP] and by M. S. Baouendi and L. P. Rothschild in [BR1] and [BR2].